You can find the speed of the ball through energy by shooting it straight up and using potential and kinetic energy and set them up to eachother. I used Kinetics by solving for time on the y direction knowning that the "only force" acting on it was gravity. after i found time i used it with the distance that it traveled.
dy= 1/2gt^2
dy= .87 m
g= 9.8 m/s^2
.87= 1/2(9.8)t^2
t=.421
v= dx/t
v= ?
dx= 2.27
t= .421
v=2.27/.421
v=5.39 m/s
(experimental-actual)/actual) x 100
((7.75-5.39)/5.39) x 100 = 43.78 % error
Procedure:
We set up the ballistic pendulum and ensured that it was calibrated so that the ball got stuck inside the pendulum. We cocked the pendulum to the first level and then released it. We measured the angles the pendulum reached. We also measured the height that it reached. We found the difference from where it started and from where it reached to. the average high that we found was .02 meters. this was then plugged in into the equation we found which solved for Vb after we found the mass of the pendulum+ball and the ball. The value we got for this was 7.75 m/s which was the experimental value. We are trying to find how close this is to the actual value. we found the actual value by find how far the ball went if shot outwards onto the ground, and finding the time. After this was found we concluded that the actual value is 5.39 m/s. After finding percent error we found that it was 43.79 % error.
Derivation
MbVb=(Mv+Mp)V
V=(MbVb)/(Mb+Mp)
1/2(Mb+Mp)V^2= (Mb+Mp)gh
1/2 (MbVb)^2/(Mb+Mp)^2=gh
Vb^2=(Mb+Mp)^2/Mb^2 2gh
Vb=((Mb+Mp)/Mb)(2gh)^(1/2)
Vb = (2gh)^(1/2)((Mb + Mp)/Mb)
h = 0.02 m
g= 9.8 m/s^2
Mb = 0.0076kg
Mp = 0.0865kg
Vb = (2(9.8)(.02))^(1/2)((0.0076+.0865)/ .0076) = 7.75
You can find the speed of the ball through energy by shooting it straight up and using potential and kinetic energy and set them up to eachother. I used Kinetics by solving for time on the y direction knowning that the "only force" acting on it was gravity. after i found time i used it with the distance that it traveled.
dy= 1/2gt^2
dy= .87 m
g= 9.8 m/s^2
.87= 1/2(9.8)t^2
t=.421
v= dx/t
v= ?
dx= 2.27
t= .421
v=2.27/.421
v=5.39 m/s
(experimental-actual)/actual) x 100
((7.75-5.39)/5.39) x 100 = 43.78 % error
Procedure:
We set up the ballistic pendulum and ensured that it was calibrated so that the ball got stuck inside the pendulum. We cocked the pendulum to the first level and then released it. We measured the angles the pendulum reached. We also measured the height that it reached. We found the difference from where it started and from where it reached to. the average high that we found was .02 meters. this was then plugged in into the equation we found which solved for Vb after we found the mass of the pendulum+ball and the ball. The value we got for this was 7.75 m/s which was the experimental value. We are trying to find how close this is to the actual value. we found the actual value by find how far the ball went if shot outwards onto the ground, and finding the time. After this was found we concluded that the actual value is 5.39 m/s. After finding percent error we found that it was 43.79 % error.